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The calculation of the conductance of disordered rings requires a theory thatgoes beyond the Kubo-Drude formulation. Assuming "mesoscopic" circumstances theanalysis of the electro-driven transitions show similarities with a percolationproblem in energy space. We argue that the texture and the sparsity of theperturbation matrix dictate the value of the conductance, and study itsdependence on the disorder strength, ranging from the ballistic to the Andersonlocalization regime. An improved sparse random matrix model is introduced tocaptures the essential ingredients of the problem, and leads to a generalizedvariable range hopping picture.

The mesoscopic conductance of disordered rings, its random matrix theory, and the generalized variable range hopping picture